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inequality

by Gurpinder » Wed Sep 01, 2010 10:00 am
how does x^2-x<0 = 0<x<1

x^2-x<0
x^2<x

and thats it......
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by albatross86 » Wed Sep 01, 2010 11:21 am
You've reached: x^2 < x

Now we know: x^2 > 0 (since all squares are going to be positive)

So if x > x^2 then obviously x is also > 0

The only interval on the number line in which x^2 happens to be less than x is in the interval 0 to 1.

For any x > 1, x^2 is ALWAYS > x

This is because from 0 to 1, exponents actually diminish. eg. 0.1^2 = 0.01, etc.

This is an important thing to remember on the GMAT so it's good that you are getting into the "WHY" :)

Cheers! Hope that helps!
~Abhay

Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide
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by Gurpinder » Wed Sep 01, 2010 11:27 am
albatross86 wrote:You've reached: x^2 < x

Now we know: x^2 > 0 (since all squares are going to be positive)

So if x > x^2 then obviously x is also > 0

The only interval on the number line in which x^2 happens to be less than x is in the interval 0 to 1.

For any x > 1, x^2 is ALWAYS > x

This is because from 0 to 1, exponents actually diminish. eg. 0.1^2 = 0.01, etc.

This is an important thing to remember on the GMAT so it's good that you are getting into the "WHY" :)

Cheers! Hope that helps!
Hey Abhay,

Ohh.....omg silly me.

Thank you!
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
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